Results 281 to 290 of about 27,139 (294)
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Analysis and Applications, 2003
We consider a subRiemannian geometry induced by a step 3 subelliptic partial differential operator in ℝ3. Our main result is the characterization of a canonical submanifold through the origin, all of whose points are connected to the origin by infinitely many (subRiemannian) geodesics.
Ovidiu Calin, Peter Greiner
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We consider a subRiemannian geometry induced by a step 3 subelliptic partial differential operator in ℝ3. Our main result is the characterization of a canonical submanifold through the origin, all of whose points are connected to the origin by infinitely many (subRiemannian) geodesics.
Ovidiu Calin, Peter Greiner
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Geometriae Dedicata, 1991
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John K. Beem, Phillip E. Parker
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
John K. Beem, Phillip E. Parker
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Geodesic as Limit of Geodesics on PL-Surfaces
2008We study the problem of convergence of geodesics on PL-surfaces and in particular on subdivision surfaces. More precisely, if a sequence (Tn)n∈N of PL-surfaces converges in distance and in normals to a smooth surface S and if Cn is a geodesic of Tn (i.e.
André Lieutier, Boris Thibert
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Hamilton–Jacobi formalism for geodesics and geodesic deviations
Journal of Mathematical Physics, 1989A formalism of integrating the equations of geodesics and of geodesic deviation is examined based upon the Hamilton–Jacobi equation for geodesics. The latter equation has been extended to the case of geodesic deviation and theorems analogous to Jacobi’s theorem on the complete integral has been proved.
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Journal of Graph Theory, 1983
AbstractDefine a geodesic subgraph of a graph to be a subgraph H with the property that any geodesic of two points of H is in H. The trivial geodesic subgraphs are the complete graphs Kn' n ≧ 0, and G itself. We characterize all (finite, simple, connected) graphs with only the trivial geodesic subgraphs, and give an algorithm for their construction. We
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AbstractDefine a geodesic subgraph of a graph to be a subgraph H with the property that any geodesic of two points of H is in H. The trivial geodesic subgraphs are the complete graphs Kn' n ≧ 0, and G itself. We characterize all (finite, simple, connected) graphs with only the trivial geodesic subgraphs, and give an algorithm for their construction. We
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1998
We are now ready to move on to the local and global geometry of Riemannian manifolds. The main tool for this will be the important concept of geodesics. These curves will help us define and understand Riemannian manifolds as metric spaces. One is led quickly to two types of “completeness”.
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We are now ready to move on to the local and global geometry of Riemannian manifolds. The main tool for this will be the important concept of geodesics. These curves will help us define and understand Riemannian manifolds as metric spaces. One is led quickly to two types of “completeness”.
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1983
In this paper a more general definition of geodesic in \(\mathbb R^n\) with respect to a given obstacle \(U\), namely on a manifold with boundary, is considered and it is shown that a classical result, obtained by Morse and Serre for a manifold without boundary (see [\textit{J.-P. Serre}, Ann. Math. (2) 54, 425--505 (1951; Zbl 0045.26003)]) holds here,
MARINO, ANTONIO, SCOLOZZI D.
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In this paper a more general definition of geodesic in \(\mathbb R^n\) with respect to a given obstacle \(U\), namely on a manifold with boundary, is considered and it is shown that a classical result, obtained by Morse and Serre for a manifold without boundary (see [\textit{J.-P. Serre}, Ann. Math. (2) 54, 425--505 (1951; Zbl 0045.26003)]) holds here,
MARINO, ANTONIO, SCOLOZZI D.
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Geodesics and geodesic circles in a geodesically convex surface: a sub-mixing property
Publicationes Mathematicae Debrecen, 2019Toshiki Kondo, Nobuhiro Innami
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